V- number or cut off frequency or normalized frequency in optical fibers is equal to

V = Пd(Numerical Aperture)/λ

Where d is the diameter of the core and λ is the wavelength of light passing through the core of the fiber.

As NA = √n1² – n2² or

NA = Sin θ or

NA = n1√2 Δ

Therefore, V number relation can be changed after putting the above relations in basic relation of V according to the need.

Significance of V number:

If V is less than 2.405 then the fiber is mono mode but if V is greater than 2.405 then fiber is multimode.

V number is also related with the number of modes is the fiber as:

N = V²/ 2 for step index fiber and

Number of modes for graded index fiber is N = V²/ 4.